Simplify the following expression: $k = \dfrac{8mn + 10n^2}{6mn + 2pn} - \dfrac{12mn - 4pn}{6mn + 2pn}$ You can assume $m,n,p \neq 0$.
Answer: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{8mn + 10n^2 - (12mn - 4pn)}{6mn + 2pn}$ $k = \dfrac{-4mn + 10n^2 + 4pn}{6mn + 2pn}$ The numerator and denominator have a common factor of $2n$, so we can simplify $k = \dfrac{-2m + 5n + 2p}{3m + p}$